Optimum beamformers for uniform circular arrays in a correlated signal environment

By virtue of their geometry, uniform circular arrays (UCAs) are ideally suited to provide 360 degrees of coverage in the azimuthal plane. However, in a correlated signal environment, the well-known technique of spatial smoothing to mitigate the signal cancellation effect as seen in an optimum beamformer will not work since this technique is applicable only to uniform linear arrays. We show how the transformation of Davies (1965) can be adopted to design optimum beamformers for UCAs in a correlated signal environment. We also introduce derivative constraints to improve the robustness of the optimum beamformers to mismatches between the beamformers´ look direction and the actual direction-of-arrival of the desired signal. The effectiveness of our design method is illustrated by a numerical example